Solve the problem.
-The revenue achieved by selling $x$ graphing calculators is figured to be $x ( 28 - 0.2 x )$ dollars. The cost of each calculator is $\$ 20$. How many graphing calculators must be sold to make a profit (revenue - cost) of at least $\$ 75.00$ ?
A) $\{ x \mid 17

Question

Solve the problem.
-The revenue achieved by selling $x$ graphing calculators is figured to be $x ( 28 - 0.2 x )$ dollars. The cost of each calculator is $\$ 20$. How many graphing calculators must be sold to make a profit (revenue - cost) of at least $\$ 75.00$ ?
A) $\{ x \mid 17 < x < 23 \}$
B) $\{ x \mid 16 < x < 14 \}$
C) $\{ x \mid 5 < x < 15 \}$
D) $\{ x \mid 15 < x < 25 \}$

Quizplus · Accepted Answer

To find the number of calculators $x$ that must be sold to make a profit of at least $75, we first express the profit equation and solve for $x$. The revenue from selling $x$ calculators is $x(28 - 0.2x)$, and the cost is $20x$ (since each calculator costs $20). The profit is thus $x(28 - 0.2x) - 20x$. Setting this equal to $75 and solving for $x$ gives us the range of $x$ that satisfies the profit condition. Simplifying the profit equation gives a quadratic equation in $x$, and solving this equation yields the range of $x$ values that result in a profit of at least $75. The correct range is $15 < x < 25$, which matches option D.

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